population lives in forest, then 60% of our sample should be in that habitat. Of
course, there is an element of circularity in this, and it depends on the reliability
of the original information. There is the added complication that numbers may
be much more variable in one habitat than in another, requiring many more
counts there to achieve the same level of precision.
In general, we can improve precision by choosing strata that minimize the
variation between sampling units within a stratum while maximizing the varia-
tion between strata. This is quite easily achieved because birds generally occur
at different densities in different habitats. As we have seen above, the simplest
choice is proportional allocation of sampling units within strata, but if the costs of
counting sampling units differs across strata, or the counts are more variable in
some strata, we can adjust our sampling to optimize allocation (Box 2.1: Snedecor
and Cochran 1980). The basic rule is to take smaller samples, compared to pro-
portional allocation, in a stratum where sampling is expensive, and to take bigger
samples in a stratum where the counts are more variable. Even rough estimates
of variability and cost can help to improve sampling design.
Problems can arise if the number of strata is large relative to the total number of
study plots (so that only a few sampling units are selected in each stratum). We
recommend using a small number of strata; 2–6 is generally sufficient. One of
the reasons for this is that a separate population estimate should be calculated
for each stratum and these estimates must be added together to get an overall
estimate of the total population. Likewise, confidence limits on these estimates
have to be found by combining information from the strata (Box 2.2;
see Wilkinson et al. 2002, Wotton et al. 2002).
In the real world, it may be very difficult to sample totally at random, for
example, because you are unable to travel long distances to remote areas to count
32 |Bird census and survey techniques
Box 2.1Choice of sample sizes within strata- Proportional allocation: Take the same fraction of sampling units from each
stratum; that is, make nh/Nhthe same for all strata - Optimum allocation: Make nhproportional to NhSh/√Ch. This delivers the
smallest standard error around an estimate for a given cost.
Where: nhis the sample size chosen in the hth stratum, Nhthe total number of
sampling units in the hth stratum, Shthe standard deviation of sampling units in the
hth stratum, and Chis the cost of sampling per sampling unit in the hth stratum.